DAVOS, SWITZERLAND – T he world’s political and business elite headed home Sunday from this year’s Davos forum with warnings that while the worst of the financial crisis seems over there is still much to be done.

International Monetary Fund chief Christine Lagarde said in the closing moments of the annual gathering in the snowy Swiss ski resort on Saturday that she recommended the “do not relax principle” for the coming year.

Where for the two previous years a sense of crisis had hung over the World Economic Forum, the mood was sunnier at the 2013 edition as speaker after speaker said they were now cautiously optimistic.

“I feel the circumstances in which I’m addressing you today are very different than 12 months ago,” said Italian Prime Minister Mario Monti in his opening speech, following a torrid year dominated by the euro crisis.

European central banker Mario Draghi meanwhile hailed 2012 as the year that the troubled single currency was “relaunched,” even as others were hailing him as the man who had saved the eurozone from catastrophe.

The Chinese economy’s slowdown seemed less serious than a year ago to the participants while the step back from the fiscal cliff in the United States also eased minds.

But as the 2,500 world leaders, financial officials, tycoons and journalists departed the picture-postcard Alpine resort, they may have felt a chill that was not just down to the subzero temperatures.

Lagarde said the IMF’s forecast of a “very fragile and timid recovery for 2013″ was based on “eurozone leaders, the U.S. authorities on the other hand and the Japanese authorities making the right decisions.”

She added: “And that’s what I mean by ‘do not relax’ because some good policy decisions have been made in various parts of the world. In 2013, they have to keep the momentum.”

The head of the Organisation for Economic Co-operation and Development, Angel Gurria, warned meanwhile that many countries had exhausted most of their room to maneuver, in terms of fiscal and monetary policy.

“We should be very worried because the lack of room for some of the more traditional tools has gone and we are left with very few of these tools,” he said.

Mood of complacency

As in previous years the Davos forum was partly hijacked by external events, particularly after British Prime Minister David Cameron vowed to hold a referendum on European Union membership by the end of 2017.

The move threatened to cause a stir, with Cameron’s European counterparts worried about the effect the uncertainty would have on the euro’s already fragile recovery, but they left any rows for another day.

The turmoil in the Arab world also took center stage for a time as officials including Jordan’s King Abdullah II urged “desperately needed” action over Syria’s civil war, though none came.

Amid the cocktail parties and lavish luncheons at Davos this year there was sometimes a “mood of complacency,” said Axel Weber, the chairman of Swiss bank UBS and former head of Germany’s Bundesbank.

“My biggest fear is that 2013 could be a replay of 2012, another lost year,” he said. “We shouldn’t be complacent, we haven’t really fundamentally improved that much.”

Many were still worried by the euro. The Deloitte financial group’s global chief executive Barry Salzberg said he was “reasonably comfortable, with one exception — and that is what’s the impact on the U.S. from Europe.”

Other officials expressed fears that governments would increasingly lean on central banks, which have often been the heroes of the fragile global recovery in the past two years, instead of taking action themselves.

But in many ways it was business as usual at Davos, with world leaders huddling in private and corporate deals sewn up on the sidelines, such as a $10 billion shale gas deal between Ukraine and oil giant Royal Dutch Shell.

Even a noisy protest on Sunday by three topless, pink-flare-waving women from a Ukrainian feminist group failed to shock — they had targeted Davos the previous year, too.